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 Izv. Akad. Nauk SSSR Ser. Mat., 1986, Volume 50, Issue 2, Pages 425–432 (Mi izv1491)

Multiple completeness in the sense of M. V. Keldysh of root functions of elliptic boundary value problems with a polynomial spectral parameter

S. Ya. Yakubov

Abstract: In spite of the fact that the theory of solvability of elliptic boundary value problems with a polynomial spectral parameter was completed in the 1960s, up till now multiple completeness of the root functions of such problems has not been proved. In this paper the author first establishes multiple completeness of the root vectors of a polynomial unbounded operator pencil that is not of Keldysh form, and then as an application the indicated gap is filled.
Bibliography: 13 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1987, 28:2, 413–420

Bibliographic databases:

UDC: 517.98
MSC: 35J40, 35P10

Citation: S. Ya. Yakubov, “Multiple completeness in the sense of M. V. Keldysh of root functions of elliptic boundary value problems with a polynomial spectral parameter”, Izv. Akad. Nauk SSSR Ser. Mat., 50:2 (1986), 425–432; Math. USSR-Izv., 28:2 (1987), 413–420

Citation in format AMSBIB
\Bibitem{Yak86} \by S.~Ya.~Yakubov \paper Multiple completeness in the sense of M.\,V.~Keldysh of root functions of elliptic boundary value problems with a~polynomial spectral parameter \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1986 \vol 50 \issue 2 \pages 425--432 \mathnet{http://mi.mathnet.ru/izv1491} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=842589} \zmath{https://zbmath.org/?q=an:0615.35061} \transl \jour Math. USSR-Izv. \yr 1987 \vol 28 \issue 2 \pages 413--420 \crossref{https://doi.org/10.1070/IM1987v028n02ABEH000890} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. S. Ya. Yakubov, “Multiple completeness for systems of operator bundles and elliptic boundary value problem”, Math. USSR-Sb., 69:1 (1991), 99–119
2. M. S. Agranovich, “Non-self-adjoint problems with a parameter that are elliptic in the sense of Agmon–Douglis–Nirenberg”, Funct. Anal. Appl., 24:1 (1990), 50–53
3. A. M. Akhtyamov, “Calculating the Coefficients of the Expansion in Derived Keldysh Chains for an Elliptic Problem with Parameter in the Boundary Condition”, Math. Notes, 69:4 (2001), 567–570
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